On the Power of Bootstrapped Specification Tests

Abstract

Decisions based on econometric model estimates may not have the expected effect if the model is misspecified. Thus, specification tests should precede any analysis. Bierens' specification test is consistent and has optimality properties against some local alternatives. A shortcoming is that the test statistic is not distribution free, even asymptotically. This makes the test unfeasible. There have been many suggestions to circumvent this problem, including the use of upper bounds for the critical values. However, these suggestions lead to tests that lose power and optimality against local alternatives. In this paper we show that bootstrap methods allow us to recover power and optimality of Bierens' original test. Bootstrap also provides reliable p-values, which have a central role in Fisher's theory of hypothesis testing. The paper also includes a discussion of the properties of the bootstrap Nonlinear Least Squares Estimator under local alternatives.

Key Words:

• Regression model
• Local alternative
• Specification test
• Stochastic process
• Wild bootstrap

JEL Classification:

• C12
• C14

Acknowledgment

The author acknowledges financial support from Asociación Mexicana de Cultura and from Consejo Nacional de Ciencia y Tecnología (CONACYT) under the project grant J38276D.

Notes

^aWe refer to the interested reader to Sec. 4 in Bierens (1990) for a brief description of this space and to references therein for a detailed treatment.